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The behavior of a Bose--Einstein condensate in a homogeneous gravitational field is analyzed. We consider two different trapping potentials. Firstly, the gas is inside a finite container. The effects of the finiteness of the height of the…
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research…
Phase transitions are ubiquitous in our three-dimensional world. By contrast most conventional transitions do not occur in infinite uniform two-dimensional systems because of the increased role of thermal fluctuations. Here we explore the…
The field of quantum turbulence is related to the manifestation of turbulence in quantum fluids, such as liquid helium and ultracold gases. The concept of turbulence in quantum systems was conceived more than 70 years ago by Onsager and…
The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The…
It has been recently claimed that dark matter could be in the form of a Bose-Einstein condensate (BEC) in order to explain the dynamics at large distances from the galactic center [Boehmer, Harko, JCAP {\bf 0706}, 025 (2007)]. In this paper…
We consider an ultracold quantum degenerate gas in an optical lattice inside a cavity. This system represents a simple but key model for "quantum optics with quantum gases," where a quantum description of both light and atomic motion is…
We present a theory of a two-component atomic Fermi gas with tunable attractive contact interactions on a spherical shell going through the Bardeen-Cooper-Schrieffer (BCS) - Bose Einstein condensation (BEC) crossover, inspired by the…
We show that current in a two-dimensional electron gas (2DEG) can trap ultracold atoms $<1 \mu$m away with orders of magnitude less spatial noise than a metal trapping wire. This enables the creation of hybrid systems, which integrate…
The paper is a continuation of our previous work on the strong convergence to equilibrium for the spatially homogeneous Boltzmann equation for Bose-Einstein particles for isotropic solutions at low temperature. Here we study the influence…
The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in two-dimensional (2D) electron-hole system embedded in a semiconductor microcavity in a high magnetic field $B$ is predicted. There are two physical realizations of 2D…
We present a pedagogical introduction to Bose-Einstein condensation in traps with spherical symmetry, namely the spherical box and the thick shell, sometimes called bubble trap. In order to obtain the critical temperature for Bose-Einstein…
We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space.…
We study the quantum dynamics of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) in a double-well potential inspired by the experimental protocol recently developed by NIST group. We focus on the regime where the number of atoms is…
We study the Bose-Einstein condensation (BEC) of a free Bose gas under rigid rotation. The aim is to explore the impact of rotation on the thermodynamic quantities associated with BEC, including the Bose-Einstein (BE) transition temperature…
OCTBEC is a Matlab toolbox designed for optimal quantum control, within the framework of optimal control theory (OCT), of Bose-Einstein condensates (BEC). The systems we have in mind are ultracold atoms in confined geometries, where the…
We examine the possibility of Bose-Einstein condensation (BEC) in two-dimensional (2D) system of interacting particles in a trap. We use a self-consistent mean-field theory of Bose particles interacting by a contact interaction in the Popov…
We reinvestigate the Bose-Einstein condensation (BEC) thermodynamics of a weakly interacting dilute Bose gas under the action of a trap using a semiclassical two-fluid mean-field model in order to find the domain of applicability of the…
Quantum vortices in the multi-component Bose-Einstein condensation (BEC) are investigated theoretically. It is found that three kinds of the vortex configurations are possible and their physical properties are discussed in details,…
After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov…